This is just a sandbox for you to work in, if you’d like. Be aware that there is no way to save your work except to cut and paste it elsewhere.

Some common commands:

`Mod(a,n)`

computes the residue of `a`

modulo `n`

. If you need to do a giant exponent, put it outside, like `Mod(a,n)^e`

so the computer does it sensibly.
`gcd(a,b)`

computes the gcd of `a`

and `b`

.
`xgcd(a,b)`

computes the extended euclidean algorithm of `a`

and `b`

(i.e. it outputs the solution to the linear Diophantine equation $ax+by=gcd(a,b)$).
`primitive_root(p)`

will give a primitive root modulo `p`

.
`next_prime(n)`

will compute the first prime after `n`

(e.g. $n+1$, $n+2$ etc.)
`is_prime(n)`

will return True if `n`

is prime, and false otherwise.
`factor(n)`

will display a factorization of `n`

.
`euler_phi(n)`

will compute the Euler phi (totient) function of `n`

.
`randint(n,m)`

will give a random integer between `n`

and `m`

inclusive.

## Fall 2024 – Professor Katherine Stange